Prerequisites
This "How To" assumes that you have a working Debian web server. Here is a good guide for perfect server.

Repositories for Debian web-server Apache/NginX
apt-get install -y apt-transport-https lsb-release ca-certificates
wget -O /etc/apt/trusted.gpg.d/php.gpg https://packages.sury.org/php/apt.gpg
echo "deb https://packages.sury.org/php/ $(lsb_release -sc) main" > /etc/apt/sources.list.d/php.list
apt-get update

Update 2021/09: DPA has a new key. You might have to upgrade with:
wget -O /etc/apt/trusted.gpg.d/php.gpg https://packages.sury.org/php/apt.gpg
apt-get update

Legacy support
apt install php-memcache php-memcached php-apcu php-apcu-bc php-mysql sqlite libsqlite3-0 php-sqlite3 php-zip php-zeroc-ice php-xml php-tcpdf php-ssh2 php-soap php-snmp php-redis php-php-gettext php-mysql php-pear php-net-smtp php-net-socket php-net-imap php-net-nntp php-mcrypt php-mbstring php-imap php-intl php-json php-imagick php-gnupg php-gd php-geoip php-fpm php-dev php-mail php-mail-mime php-curl php-auth-sasl

Currently supported php7
apt install php7.0-common php7.0-cli php7.0-cgi php7.0-fpm php7.0-gd php7.0-mbstring php7.0-mysql php7.0-sqlite3 php7.0-imap php7.0-curl php7.0-intl php7.0-pspell php7.0-sqlite3 php7.0-tidy php7.0-xmlrpc php7.0-xsl php7.0-zip php7.0-soap php7.1-common php7.1-cli php7.1-cgi php7.1-fpm php7.1-gd php7.1-mbstring php7.1-mysql php7.1-sqlite3 php7.1-imap php7.1-curl php7.1-intl php7.1-pspell php7.1-sqlite3 php7.1-tidy php7.1-xmlrpc php7.1-xsl php7.1-zip php7.1-soap php7.2-common php7.2-cli php7.2-cgi php7.2-fpm php7.2-gd php7.2-mbstring php7.2-mysql php7.2-sqlite3 php7.2-imap php7.2-curl php7.2-intl php7.2-pspell php7.2-sqlite3 php7.2-tidy php7.2-xmlrpc php7.2-xsl php7.2-zip php7.2-soap php7.3-common php7.3-cli php7.3-cgi php7.3-fpm php7.3-gd php7.3-mbstring php7.3-mysql php7.3-sqlite3 php7.3-imap php7.3-curl php7.3-intl php7.3-pspell php7.3-sqlite3 php7.3-tidy php7.3-xmlrpc php7.3-xsl php7.3-zip php7.3-soap php7.4-common php7.4-cli php7.4-cgi php7.4-fpm php7.4-gd php7.4-mbstring php7.4-mysql php7.4-sqlite3 php7.4-imap php7.4-curl php7.4-intl php7.4-pspell php7.4-sqlite3 php7.4-tidy php7.4-xmlrpc php7.4-xsl php7.4-zip php7.4-soap

New php8
apt install php8.0-common php8.0-cli php8.0-cgi php8.0-fpm php8.0-gd php8.0-mbstring php8.0-mysql php8.0-sqlite3 php8.0-imap php8.0-curl php8.0-intl php8.0-pspell php8.0-sqlite3 php8.0-tidy php8.0-xmlrpc php8.0-xsl php8.0-zip php8.0-soap

No longer supported
apt install php7.?-mcrypt php7.?-recode

Enable new services
systemctl enable php7.0-fpm
systemctl enable php7.1-fpm
systemctl enable php7.2-fpm
systemctl enable php7.3-fpm
systemctl enable php7.4-fpm

systemctl enable php8.0-fpm
a2enconf php8.0-fpm

a2enmod proxy_fcgi setenvif

Activate the necessary Apache modules
a2enmod suexec rewrite ssl actions include cgi dav_fs dav auth_digest headers proxy_fcgi alias

Set Default PHP to 7.0
update-alternatives --config php
update-alternatives --config php-cgi

Mandatory commands
systemctl restart php*
systemctl restart apache2.service

Helpful diagnostic commands
systemctl status php7*
systemctl status apache2.service
systemctl status php7.0-fpm.service
systemctl enable php7.4-fpm

systemctl status php8*
systemctl status apache2.service
systemctl status php8.0-fpm.service
systemctl enable php8.0-fpm

Notes
You should keep the default PHP version as 7.0 or many 3rd party services like ISPConfig may fail to start.

ISPConfig related - Additional PHP Versions
These settings are found in ISPConfig System Settings
(Leave Client field empty!)

PHP Name: PHP 7.0
FastCGI Settings: 
Path to the PHP FastCGI binary: php-cgi7.0
Path to the php.ini directory: /etc/php/7.0/cgi/php.ini
PHP-FPM Settings: 
Path to the PHP-FPM init script: php7.0-fpm
Path to the php.ini directory: /etc/php/7.0/fpm/php.ini
Path to the PHP-FPM pool directory: /etc/php/7.0/fpm/pool.d

PHP Name: PHP 7.1
FastCGI Settings: 
Path to the PHP FastCGI binary: php-cgi7.1
Path to the php.ini directory: /etc/php/7.1/cgi/php.ini
PHP-FPM Settings: 
Path to the PHP-FPM init script: php7.1-fpm
Path to the php.ini directory: /etc/php/7.1/fpm/php.ini
Path to the PHP-FPM pool directory: /etc/php/7.1/fpm/pool.d

PHP Name: PHP 7.2
FastCGI Settings: 
Path to the PHP FastCGI binary: php-cgi7.2
Path to the php.ini directory: /etc/php/7.2/cgi/php.ini
PHP-FPM Settings: 
Path to the PHP-FPM init script: php7.2-fpm
Path to the php.ini directory: /etc/php/7.2/fpm/php.ini
Path to the PHP-FPM pool directory: /etc/php/7.2/fpm/pool.d

PHP Name: PHP 7.3
FastCGI Settings: 
Path to the PHP FastCGI binary: php-cgi7.3
Path to the php.ini directory: /etc/php/7.3/cgi/php.ini
PHP-FPM Settings: 
Path to the PHP-FPM init script: php7.3-fpm
Path to the php.ini directory: /etc/php/7.3/fpm/php.ini
Path to the PHP-FPM pool directory: /etc/php/7.3/fpm/pool.d

PHP Name: PHP 7.4
FastCGI Settings: 
Path to the PHP FastCGI binary: php-cgi7.4
Path to the php.ini directory: /etc/php/7.4/cgi/php.ini
PHP-FPM Settings: 
Path to the PHP-FPM init script: php7.4-fpm
Path to the php.ini directory: /etc/php/7.4/fpm/php.ini
Path to the PHP-FPM pool directory: /etc/php/7.4/fpm/pool.d